Gini and optimal income taxation by rank

We solve the non-linear income tax program for a rank-dependent social welfare function à la Yaari, expressing the trade-off between size and inequality using the Gini or related families of positional indices. The key idea is that when agents optimize and absent bunching, ranks in the actual and optimal allocations become an invariant dimension. This allows us to obtain optimal marginal tax rates as a function of ranks, and numerically illustrate the relationship between ranks and taxes. For singles without children, the actual US tax schedule seems to indicate a distaste for differences in the upper part of the distribution.